The present disclosure relates to systems and methods of imaging. More particularly, the present disclosure relates to systems and methods of imaging that employ coded excitation with mismatched codes.
In the field of biomedical ultrasound (ultrasound) imaging, in which phased array transducers with several elements are used for transmission and detection of ultrasound signal, different approaches have been proposed to achieve high-frame-rate ultrasound imaging while preserving image quality. Parallel beamforming or multi-line transmission is a method based on generating a spherical wave by transmitting a diverging beam from multiple elements, which is also called “explososcan” (Shattuck, et. al J. Acoust. Soc. Am. 1984; 75(4): 1273-1282) (von Ramm, et al., IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1991; 38(2): 109-115) (Hergum, et. al, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2007; 54(2): 271-280) (Madore, et. al, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2009; 56(12): 2612-2623).
Similarly, there were attempts to perform fast volumetric ultrasound imaging by multiple beams (Bredthauer and von Ramm, IEEE Int. Symp. Biomedical Imaging; 2002). The complexity of those systems was fairly high, however, they enabled 3D imaging. Parallel beamforming can also be used to generate a plane wave beam. Plane-wave compounding is shown to be an effective method for high-frame-rate imaging (Montaldo, et. al, IEEE Trans. Ultrason. Ferr. Freq. Contr. 2009; 56(3): 489-506) (Mallart and Fink, Proc. SPIE 1730, 1992: 120-130) (Tanter and Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2014; 61(1): 102-119).
Another promising method is multiple-element synthetic aperture imaging (SAI) which can increase the frame rate while reducing system complexity (Jensen, et. al, Ultrasonics J. 2006; 44: e5-e15) (Karaman, et. al, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1995; 42: 429-442). Many different techniques have been employed to perform multiple transmissions in the SAI method with combination of coded excitations.
There are two main types of coded excitations, frequency-coded and phase-coded signals. The most popular frequency-coding is linear frequency modulation, and examples of phase-coding are Golay codes and Barker codes. One common technique was based on choosing long independent Golay codes (Golay Code) or m-sequences, to minimize the cross-correlation (cross-correlation) between the signals (Kiymik, et. al, Signal Processing. 1997; 58: 107-113) (Shen and Ebbini, IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1996; 43: p. 131-140). It was also shown that, by employing the equivalence properties of Golay Codes, a set of Golay Codes can be generated in a way that while their cross-correlations are nonzero, the summation of cross-correlations of complementary codes cancels each other out (Lee and Furgason, Ultrasonics Symposium. 1982: 821-825). The same technique was also used for multiple-spectral photoacoustic imaging (Mienkina et al., Optics Express, 2010; 18(9): 9076-9087). The other techniques employed the Hadamard decoding method (Chiao, et. al, IEEE Ultrasonics Symposium. 1997; 2: 1679-1682.) or a combination of Hadamard decoding and dissimilar Golay Codes (ultrasound U.S. Pat. No. 6,048,315, 2000) (Chiao and Thomas, Proc. IEEE Ultrason. Symp. 2000: 1677-1680). Hadamard decoding has been widely used to generate orthogonal codes with Golay Codes (Yang et. al, IEEE International Symposium on Circuits and Systems (ISCAS). 2012: 113-116).
Various methods have been suggested to generate mismatched codes with frequency modulation (FM) signals as well. Misaridis and Jensen have suggested employing two chirps with similar duration and bandwidth but with opposite slopes, however the method is limited to only two codes and therefore fails to be practical in many applications (Misaridis and Jensen, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 2005:52(2), 207-218).
Other methods that have been employed to generate multiple mismatched codes are either dissimilar durations among different codes, or dissimilar frequency ranges among different codes (the frequency ranges of the different codes may overlap but cannot be identical). A linear frequency sweep per each of dissimilar frequency ranges or per each of dissimilar durations produces a frequency slope different from others. However, the disadvantage is that each of those unique frequency modulations also has a unique signal-to-noise ratio (SNR) and resolution. It should be clarified that the frequency sweeps employed in these other methods consist of only one linear frequency sweep per code (see FIG. 16A). Therefore, the durations mentioned above refer to total frequency code length (i.e. there is no sub-chirp) (Misaridis, and, Jensen, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 2005: 52(2), 207-218.). Therefore, these methods result in non-uniform signal-to-noise ratios (SNR) and resolutions.
Hadamard decoding has also been employed with up- and down-sweep chirps to generate a set of orthogonal codes (Misaridis and Jensen, Ultrasonics. 2002; 40: 593-597).
Alternatively, the bandwidth can be divided into several parts, so that, multiple excitation signals cover different parts of the bandwidth. The excitations can be single frequency waveforms or chirps (Gran and Jensen, SPIE Proc. 2005; 5750: 405-416) (Grant and Jensen, IEEE Ultrasonic Symposium. 2003: 1942-1946) (Behar and Adam, Ultrasonics. 2005; 43: 777-788). The combination of frequency spectrum dividing and opposite slopes has also been proposed to generate multiple focal points by simultaneous multiple transmissions (ultrasound U.S. Pat. No. 7,066,886 B2).
It should be added that very similar methods have been employed in other fields such as radar, sonar, and even wireless communications. These methods are readily applicable to biomedical ultrasound imaging. A proposed method for sonar multibeam imaging is frequency hopping (Jaffe and Cassereau, J. Acoust. Soc. Am. 1988; 83(4): 1458-1464). The bandwidth is divided into a number of individual frequencies; then, these frequencies are distributed distinctively using a frequency hopping code to produce uncorrelated waveforms. Using long mismatched pseudonoise (PN) sequences has also been suggested for multiple transmission radar imaging (Sakamoto and Sato, IEEE Transactions on Geoscience and Remote Sensing. 2009; 47(4): 1179-1186.). The Hadamard encoding technique has been extensively employed in communication phase array antennas (Silverstein, IEEE Trans. Sig. Proc. 1997; 45(1): 206-218) (Purdy, IEEE Proceedings of the Radar Conference. 1999: 172-176). Also, methods similar to parallel beamforming has been employed in MRI (Griswold, et. al, Magn Reson Med. 1999; 41: 1236-1245).
A related scheme was suggested by El-Khamy et al. (El-Khamy, et. al, IEEE 4th International Conference on Spread-Spectrum Systems and Techniques, 1996; 1209-1213) (El-Khamy, et. al, Proceedings of the Sixteenth National Radio Science Conference, NRSC '99. 1999; C6/1-C6/8). These authors divided the chirp duration into two halves, each having a separate and non-overlapping bandwidth, and swept the frequency range with two different slopes to obtain identical time and bandwidth. It should be clarified that the frequency range has been swept only once in this method but with two different slopes in the two parts of the bandwidth (e.g., as shown in FIG. 16B). The drawback of this method is that the frequency sweeps are nonlinear and non-uniform, and therefore the method fails to generate uniform signal-to-noise ratio and resolution. The advantage, on the other hand, is that there is no limitation in the number of the possible mismatched codes.
Another attempt to increase the lateral resolution without sacrificing the frame rate was through “multi-beam simultaneous multi-zone focusing method” (Kim and Song, Proc. SPIE, 2004; 5373, 315-323) (Hwang and Song, U.S. Pat. No. 6,547,733 B2, 2003). This method was implemented by combining M orthogonal GCs with L orthogonal chirps to obtain M scan lines; each consists of L different focusing depths. The orthogonal GCs had a similar number of bits and selected as described by Chiao and Thomas (Chiao and Thomas, Proc. IEEE Ultrason. Symp. 2000: 1677-1680). The orthogonal chirps were generated by dividing the frequency bandwidth of the transducer. Examples were presented for the case M=L=2 (Kim and Song, Proc. SPIE, 2004; 5373, 315-323).
To prevent the mixing of group signals, Cook suggested the use of V-FM signals (C. E. Cook, IEEE Trans. Aerosp. Electron. Syst., 1974: 10(4), 471-478). When for instance beacon codes can be transmitted; the first arm of the V-FM can be used to transmit the synchronization signal and the second arm for the message signal. It is similar to transmitting two LFM chirps with different slopes where the first slope (down-chirp) identifies the type of the message (e.g. altitude, heading, etc.) and the second LFM (up-chirp) for the data.